Tool to use a linear feedback shift register or LFSR and generate pseudo-random bits using XOR exclusive OR operations.
Linear Feedback Shift Register - dCode
Tag(s) : Informatics
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Linear Feedback Shift Register
LFSR Bits Generator
Answers to Questions (FAQ)
What is a linear feedback shift register? (Definition)
A linear feedback shift register or LFSR is a system that generates bits from a register and a feedback function.
After several iterations, the register returns to a previous state already known and starts again in a loop, the number of iterations of which is called its period.
In practice, this kind of LFSR register is useful in cryptography because it allows the generation of pseudo-random numbers when the period is long enough.
How does a LFSR work?
From the current state of the binary register, a bit selection is chosen to apply an XOR operation to it.
The result is then concatenated at the start of the register (on the left) while the final value (on the right) is deleted from the register and displayed at the output.
Example: The register is 1010, an XOR ⊕ is applied to bits 0 and 2 (numbered from left to right starting from 0)
| Step | Register | XOR | Output |
|---|---|---|---|
| 0 | _______0101 | 0 ⊕ 0 = 0 | |
| 1 | ______0010_ | 0 ⊕ 1 = 1 | 1 |
| 2 | _____1001__ | 1 ⊕ 0 = 1 | 0 |
| 3 | ____1100___ | 1 ⊕ 0 = 1 | 1 |
| 4 | ___1110____ | 1 ⊕ 1 = 0 | 0 |
| 5 | __0111_____ | 0 ⊕ 1 = 1 | 0 |
| 6 | _1011______ | 0 ⊕ 1 = 1 | 1 |
| 7 | 0101_______ | 0 ⊕ 0 = 0 | 1 |
How to use a LFSR?
To use an LFSR, the user must configure the register length, determine the initial configuration of the flip-flops, choose an appropriate linear feedback function (XOR), and specify the number of iterations/cycles needed to generate the desired sequence.
How to calculate the period of an LFSR?
The period of an LFSR is the number of iterations necessary for the generated sequence to return to its initial state.
If the register is at maximum feedback, there is no repetition, except after 2^n - 1 iteration, with n the length of the register.
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